Question

find the length of the line segment between point a and point b.
what is the length of the line segment between point a and point b? use square root notation to write the exact value of the length of the line segment. solve on paper if youd like, then enter your answer on zearn.
keep in mind, you can think of this line segment as the hypotenuse of a right triangle to help you solve.
a (-3,5)
b (6, -3)

Explanation:

Step1: Find horizontal and vertical distances

The coordinates of A are \((-3, 5)\) and B are \((6, -3)\). The horizontal distance (difference in x - coordinates) is \(6 - (-3)=9\). The vertical distance (difference in y - coordinates) is \(-3 - 5=-8\), and the absolute value is \(8\).

Step2: Apply Pythagorean theorem

The length \(d\) of the line segment (hypotenuse) is given by \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Substituting the values, we get \(d=\sqrt{(9)^2+( - 8)^2}=\sqrt{81 + 64}=\sqrt{145}\).

Answer:

\(\sqrt{145}\)